14 problems

Hutchings's Ruelle-invariant limit conjecture for ECH capacities
arXiv@arxiv
Let $(X,\omega)$ be a star-shaped domain in $\mathbb{R}^4$ , and let … be the error terms of its ECH capacities. If $(X,\omega)$ is generic, then Hutchings's Ruelle-invariant limit…
Conjectureopendynamical-systems ech-capacities symplectic-geometry
2
Unobstructedness conjecture for ellipsoid embeddings into $H_b$
arXiv@arxiv
Unobstructedness conjecture. The function $c_b(z)$ is unobstructed for $z<z_[\infty^b$ if and only if $b=m/d$ for some $(d;m;p,q)\in (H)$ .
Conjectureopenech-capacities ellipsoid-embeddings symplectic-embeddings
0
Ruelle's conjecture on the constant term in the alternative ECH capacity asymptotics
arXiv@arxiv
Ruelle's conjecture. Generically, the $O(1)$ term limits to $-1/2$ times the Ruelle invariant.
Conjectureopendynamical-systems ech-capacities symplectic-geometry
0
The higher special-point obstruction conjecture
arXiv@arxiv
Higher special-point obstruction conjecture. For $i>1$ , $c_{H_b}$ has no descending staircase. Furthermore, there exists $\varepsilon>0$ such that, for
Conjectureopenech-capacities staircases symplectic-geometry
2
The obstruction conjecture for special rational staircases
arXiv@arxiv
Obstruction conjecture for special rational staircases. For all such special $b$ , the capacity function should be given by this obstruction at points just above the corresponding s…
Conjectureopenech-capacities staircases symplectic-geometry
0
Equality of the elementary and ECH capacities for four-dimensional Liouville domains
arXiv@arxiv
Equality conjecture. For every $k$ ,
Conjectureopenech-capacities symplectic-capacities symplectic-geometry
1
Hutchings's bounded-error conjecture for ECH capacities of star-shaped domains
arXiv@arxiv
Hutchings's bounded-error conjecture. One has
Conjectureopenech-capacities symplectic-geometry
0
The tightly-constrained convex lattice domain conjecture
arXiv@arxiv
Tightly-constrained domain conjecture.
Conjectureopenech-capacities symplectic-geometry toric-domains
0
The equality conjecture for ECH and algebraic capacities
arXiv@arxiv
ECH–algebraic capacity equality conjecture. Equality
Conjectureopenech-capacities rational-surfaces symplectic-geometry
0
Hutchings's convergence conjecture for ECH error terms
arXiv@arxiv
Hutchings's convergence conjecture. For generic $\Omega$ , the sequence $e_k(X_\Omega)$ converges. The cases considered in this paper are among those that are non-generic.
Conjectureopenech-capacities symplectic-geometry
0
Bounded ECH-capacity error and the Ruelle invariant for star-shaped domains
arXiv@arxiv
Let $X$ be a nice star-shaped domain in ${\mathbb R}^4$ , and let $e_k(X)$ be the error term in the asymptotic formula for the ECH capacities of $X$ . Let $\operatorname{Ru}(X)$ be t…
Conjectureopencontact-geometry ech-capacities symplectic-geometry
0
The Ruelle invariant conjecture for ECH capacities of generic star-shaped domains
arXiv@arxiv
Let $X$ be a nice star-shaped domain in ${\mathbb R}^4$ . Write $e_k(X)$ for the error term in the asymptotic formula recovering the volume of $X$ from its ECH capacities, and let…
Conjectureopencontact-geometry ech-capacities symplectic-geometry
1
The exact quasipolynomial conjecture for ECH capacities of tightly constrained toric domains
arXiv@arxiv
Exact quasipolynomial conjecture. The word “eventually” can be removed from the asymptotic formulas: for every $r\in\{0,1,\dots,\lambda-1\}$ and every $x\in\mathbb{Z}_{\geq0}$ ,
Conjectureopenech-capacities ehrhart-theory toric-varieties
1
The weight-gcd conjecture for tightly constrained convex toric domains
arXiv@arxiv
Weight-gcd conjecture. If
Conjectureopenech-capacities symplectic-geometry toric-domains
0